Louisiana Republican Rep. Vance McAllister with his wife, Kelly, as he's sworn in by Speaker John Boehner.

J. Scott Applewhite/AP

As of this writing, Rep. Vance McAllister is still a Republican congressman representing his northeastern Louisiana district.

And that's part of the problem, according to the Louisiana Republican Party establishment. Gov. Bobby Jindal and state party chairman Roger Villere both recommended publicly and strongly that McAllister immediately resign in the wake of widely seen security video showing the married congressman canoodling a married now-ex-staffer.

As the week ended, with Congress entering its two-week spring break, McAllister was keeping a low public profile, though he did tell the News-Star newspaper of Monroe, La., earlier in the week he didn't plan to resign.

And that's the other part of the problem for the national and state Republican establishment. If McAllister, who won a November special election to get to Congress, doesn't decide to resign, his party is stuck with him. That is at least until the fall election, when voters will have their opportunity to turn him out of office.

While it's certainly a scandal for a married congressman to be captured kissing a married aide on a viral video, it certainly doesn't rise to the level of the kind of behavior that has historically caused the House to expel its members.

In fact, only five House members have gotten expelled in the nation's history, and three of those expulsions happened during the Civil War for reasons of disloyalty to the United States, according to a 2012 Congressional Research Service report. Two others, in 1980 and 2002, came after corruption convictions.

McAllister will likely face rising pressure to resign, however. Fundraising should be much harder for him now with the state party establishment firmly against him. State party officials already had reasons to feel tepid about him since he had shown an independent streak. For instance, he opposed Jindal's decision to not expand Medicaid under the Affordable Care Act; McAllister represents a district high in poverty.

Meanwhile, his newfound political weakness invites challengers who might have otherwise stayed out of the race.

Congressional Republicans like Speaker John Boehner have been more circumspect. They haven't openly called for his resignation, but they also have indicated that they expect much better behavior from members of Congress. They certainly don't appreciate the distraction caused by McAllister's case.

Just because they can't expel him doesn't mean House Republicans can't try to make life more miserable for him in the hope that he resigns, or to signal voters in his district that they might want to have someone else represent them.

For instance, they could strip him of his agriculture and natural resources committee assignments. That could truly sting, since his district is mostly rural.